I have a weightlifting spreadsheet with weight on the vertical axis and reps on the horizontal axis. The value of each cell is the estimated 1 rep max if I accomplish that lift. In theory if my e1RM is 100kg then I can lift any permutation of (weight,reps) that have the same e1RM. This is akin to knowing Pareto Frontier of my current strength.
I use conditional formatting to color cells according to the probability that I can lift them—if I lifted 50kg for 10 reps then I can definitely do 50kg for 9 reps, so that cell is green. But if e1RM(50,10) > e1RM(40,15) then I can probably do that too so it's light green. The visualization naturally becomes Pareto-like.
If I'm feeling strong I can aim for higher weight, lower reps. Or if I'm feeling weak I can close out a (weight, reps) that's below my current e1RM but I haven't accomplished yet. The end result is that I'm always "accomplishing" some sort of PR no matter how I feel.
I call this e1RM Bingo.
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Aachen
Misread the title and got excited about a Pareto font, that is, the best possible font (presumably: distinct l/I, O/0, scores within error margins of the top readability and reading speed scores, widely available, etc.)
Maybe in vein but did anyone already figure this one out? The closest I got was PT sans, open-licensed commissioned by the Russian ministry for communication (I found it surprising that a country that doesn't use Latin script made the best font!), but it's not widely shipped so you need to figure out how to include font files whenever you want to use it
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CodeIsTheEnd
I am training for a marathon, and, as I increase both by distance and pace, I am always excited when I have a "Pareto run": a run along the Pareto frontier of me trying to maximize distance and speed.
When explaining it to some coworkers, I stumbled on a fairly intuitive explanation: "I've run farther before, and I've run faster before, but I've never run _this_ far, _this fast."
There was some pushback about why not just call it a PR (personal record), but I would only use that term for fixed distances (1mi, 5k, 10k, etc.) or a consistent route that I've run many times before. Nobody would say "I set my 7.40 mile PR today." More importantly, it misses the comparison to all farther (and faster) runs—it's not exciting to set a 5k PR just because you've barely run that distance before, and the pace is actually slower that a 10k you've done.
(Had a Pareto run of 7.40 miles @ 6:28/mi last week!)
ChatGPT 5.6 Luna on the right (cheaper) cover most of the frontier, with a point for Deepseek flash, and higher performance overlapping heavily between 5.6 Sol and Fable.
That DeepSeek point will probably move back towards Luna as deepseek announced a "significant" price increase coming to their API [1], which kind of demonstrates that beating the Pareto frontier is where the difficulty actually is).
Pareto front sounds like an interesting way to optimize, but it suffers from the curse of dimensionality just like anything else.
As the number of objectives (dimensions) increases, the number of samples you need to cover the frontier increases exponentially. You will very rarely find solutions that actually dominate other solutions in many practical optimization scenarios. With 2 dimensions you have a 25% chance of domination. With 10 dimensions it's a .098% chance.
The most useful cases I've seen tend to occur where we just optimize for two things at once. The chances of domination are high, it's easy to visualize and very efficient to implement. As we get into higher dimensional spaces, things get weird really fast.
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shermantanktop
I’m sadly twitchy when I hear “Pareto” - having endured numerous middle managers suggesting they can deliver 80% of the scope in 20% of the time (unrelated to the frontier topic here). Do that at each level of an org and the nonsense multiples rapidly.
The 80/20 “rule,” as far as I know, is meant to be descriptive after the fact. It can’t be used as a planning assumption. To be fair to those managers, they don’t really mean to be rigorous. They are just trying to justify cutting scope.
If one option is at least as good on every relevant dimension and better on one, just pick it. That's not really a trade-off, and it shouldn't need escalation. Eg, if two SaaS tools cost the same and have similar support, but one fits your use case better, you choose that one. Otherwise, you just suck at your job!
The interesting decisions only start once you're already on the frontier, where getting more of one thing means giving up something else. If the better tool costs 50% more, now you're trading capability against cost, and that may need sign-off.
Basically, everyone should be able to get to the frontier on their own. Coordination and arbitration at higher levels of the org / between different departments should happen on the frontier, where the trade-offs involve several people or teams.
joncrane
Question: in auto racing, could one have a Pareto Front balancing single lap pace (qualifying optimization) and race pace (pace over an entire stint of e.g. 20+ laps)?
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lorey
Found this to display the optimal LLM choice while building evalry. It's such a useful tool, not only for thinking about it, but for visualization, too.
I'm assuming you must have discovered this through the OpenRouter LLM performance graphs.
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vavikk
Nice, this is exactly what I use for the multi-objective optimizer on a quantum network simulator I'm building — scoring topologies on fidelity/latency/success rate tradeoffs.
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hnfwd5lqmp
Simple idea, big payoff
stevefan1999
I wonder why LLM love this word so much. Same as mint, seam, tier.
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chermi
We used to just call that efficiency. Overusage of "pareto frontier" annoys me almost as much people talking about "electrons" instead of just saying electricity or power.
solomonb
Now I want a hat with the Agnostic Front logo but that says Pareto Front.
voidhorse
One nuance that people sometimes miss is that pareto optimality in the continuous case and discrete case are distinct. Using continuous case algorithms on discrete feasible set optimization problems will make you miss the interior optimal points--only extremal/supported points on the positive orthant hull are identified by the continuous algos.
Matthias Ehrgott's books on multicriteria optimization explain Pareto efficiency very well without sacrificing rigor. I think they do a better job than this article.
I have a weightlifting spreadsheet with weight on the vertical axis and reps on the horizontal axis. The value of each cell is the estimated 1 rep max if I accomplish that lift. In theory if my e1RM is 100kg then I can lift any permutation of (weight,reps) that have the same e1RM. This is akin to knowing Pareto Frontier of my current strength.
I use conditional formatting to color cells according to the probability that I can lift them—if I lifted 50kg for 10 reps then I can definitely do 50kg for 9 reps, so that cell is green. But if e1RM(50,10) > e1RM(40,15) then I can probably do that too so it's light green. The visualization naturally becomes Pareto-like.
If I'm feeling strong I can aim for higher weight, lower reps. Or if I'm feeling weak I can close out a (weight, reps) that's below my current e1RM but I haven't accomplished yet. The end result is that I'm always "accomplishing" some sort of PR no matter how I feel.
I call this e1RM Bingo.
Misread the title and got excited about a Pareto font, that is, the best possible font (presumably: distinct l/I, O/0, scores within error margins of the top readability and reading speed scores, widely available, etc.)
Maybe in vein but did anyone already figure this one out? The closest I got was PT sans, open-licensed commissioned by the Russian ministry for communication (I found it surprising that a country that doesn't use Latin script made the best font!), but it's not widely shipped so you need to figure out how to include font files whenever you want to use it
I am training for a marathon, and, as I increase both by distance and pace, I am always excited when I have a "Pareto run": a run along the Pareto frontier of me trying to maximize distance and speed.
When explaining it to some coworkers, I stumbled on a fairly intuitive explanation: "I've run farther before, and I've run faster before, but I've never run _this_ far, _this fast."
There was some pushback about why not just call it a PR (personal record), but I would only use that term for fixed distances (1mi, 5k, 10k, etc.) or a consistent route that I've run many times before. Nobody would say "I set my 7.40 mile PR today." More importantly, it misses the comparison to all farther (and faster) runs—it's not exciting to set a 5k PR just because you've barely run that distance before, and the pace is actually slower that a 10k you've done.
(Had a Pareto run of 7.40 miles @ 6:28/mi last week!)
You can see the Pareto Frontier well in DeepSWE's chart here - https://deepswe.datacurve.ai/
ChatGPT 5.6 Luna on the right (cheaper) cover most of the frontier, with a point for Deepseek flash, and higher performance overlapping heavily between 5.6 Sol and Fable.
That DeepSeek point will probably move back towards Luna as deepseek announced a "significant" price increase coming to their API [1], which kind of demonstrates that beating the Pareto frontier is where the difficulty actually is).
[1] https://www.bloomberg.com/news/articles/2026-08-06/deepseek-...
Pareto front sounds like an interesting way to optimize, but it suffers from the curse of dimensionality just like anything else.
As the number of objectives (dimensions) increases, the number of samples you need to cover the frontier increases exponentially. You will very rarely find solutions that actually dominate other solutions in many practical optimization scenarios. With 2 dimensions you have a 25% chance of domination. With 10 dimensions it's a .098% chance.
The most useful cases I've seen tend to occur where we just optimize for two things at once. The chances of domination are high, it's easy to visualize and very efficient to implement. As we get into higher dimensional spaces, things get weird really fast.
I’m sadly twitchy when I hear “Pareto” - having endured numerous middle managers suggesting they can deliver 80% of the scope in 20% of the time (unrelated to the frontier topic here). Do that at each level of an org and the nonsense multiples rapidly.
The 80/20 “rule,” as far as I know, is meant to be descriptive after the fact. It can’t be used as a planning assumption. To be fair to those managers, they don’t really mean to be rigorous. They are just trying to justify cutting scope.
https://www.mayerowitz.io/blog/mario-meets-pareto
At $JOB, I use the Pareto frontier all the time.
If one option is at least as good on every relevant dimension and better on one, just pick it. That's not really a trade-off, and it shouldn't need escalation. Eg, if two SaaS tools cost the same and have similar support, but one fits your use case better, you choose that one. Otherwise, you just suck at your job!
The interesting decisions only start once you're already on the frontier, where getting more of one thing means giving up something else. If the better tool costs 50% more, now you're trading capability against cost, and that may need sign-off.
Basically, everyone should be able to get to the frontier on their own. Coordination and arbitration at higher levels of the org / between different departments should happen on the frontier, where the trade-offs involve several people or teams.
Question: in auto racing, could one have a Pareto Front balancing single lap pace (qualifying optimization) and race pace (pace over an entire stint of e.g. 20+ laps)?
Found this to display the optimal LLM choice while building evalry. It's such a useful tool, not only for thinking about it, but for visualization, too.
Example: Which LLM gives me the best ELI5 explanations for a given price. https://evalry.com/benchmarks/explain-like-i-m-5-321
I'm assuming you must have discovered this through the OpenRouter LLM performance graphs.
Nice, this is exactly what I use for the multi-objective optimizer on a quantum network simulator I'm building — scoring topologies on fidelity/latency/success rate tradeoffs.
Simple idea, big payoff
I wonder why LLM love this word so much. Same as mint, seam, tier.
We used to just call that efficiency. Overusage of "pareto frontier" annoys me almost as much people talking about "electrons" instead of just saying electricity or power.
Now I want a hat with the Agnostic Front logo but that says Pareto Front.
One nuance that people sometimes miss is that pareto optimality in the continuous case and discrete case are distinct. Using continuous case algorithms on discrete feasible set optimization problems will make you miss the interior optimal points--only extremal/supported points on the positive orthant hull are identified by the continuous algos.
Matthias Ehrgott's books on multicriteria optimization explain Pareto efficiency very well without sacrificing rigor. I think they do a better job than this article.
may, anyone explain what is this
The lesson landed